For uncertainty calculation of any measured  parameters,refer 'experimental methods for engineers" book written by J.P.Holman.

Given that turbulence is chaotic and varies with time, it would be informative to measure the turbulent intensity over time and quantifying this range could be quoted as an uncertainty. 

The uncertainty of the mean of a turbulent variable and the uncertainty of its variance can be estimated using the integral time scale.  Suggest looking that up in turbulence text - eg, Kaimal and Finnigan.

The uncertainty of turbulence standards deviation can be estimated using the time scale integral .The uncertainty of the mean value of a it would be variable.

It depends on what you are calling "turbulence intensity".  

If you are simply referring to magnitudes of turbulent fluctuations (via e.g. second moments), then you can start by following Chris Fairall's advice (though I would instead recommend the textbook Atmospheric Turbulence by Wyngaard [2010], and possibly also the Lenschow et al article which it references). 

If you are referring to the ratio of an rms value by its mean, as common in e.g. wind engineering (sigmau / U), then the above is ok to good approximation; but you might also consider work that directly deals with such, e.g. Dimitrov, Natarajan + Kelly (2014-).

See this paper. It explains the problem well and gives practical tools.

Article Towards better uncertainty estimates for turbulence statistics

Minseop, you possibly should first specify how you understand turbulence intensity. If it is turbulent kinetic energy then we have a theory based on first principles (without use of empirical data) which gives the fundamental constants of turbulence at high Reynolds numbers with surprising accuracy. E.g. the Karman constant appears there as 1/SQRT(2*Pi) = 0.399 which is close to the international standard value and also close to the most recent Princeton-superpipe results: 0.40 +/- 0.02. There are results for finite Reynolds numbers avaiable and even for non-Newtonian fluids with some industrial success. I attach the primary paper. For more info you may contact me directly.

Article Universal equations and constants of turbulent motion

I have the same problem. Could you share how to deal with this problem? Or, give me some advice or reference. Thanks a lot!